Related Experiment Video
Updated: Jun 5, 2025
00:07
A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
Published on: September 5, 2019
8.4K
Bernoulli polynomials for a new subclass of Te-univalent functions
G Saravanan1, S Baskaran2, B Vanithakumari3,2
1Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, Jordan.
Heliyon
|December 16, 2024
Summary
This study introduces a new subclass of Te-univalent functions using Bernoulli polynomials. Key findings include coefficient bounds and the Fekete-Szegö inequality for this novel function class.
Area of Science:
- Complex Analysis
- Geometric Function Theory
Background:
- Te-univalent functions are a significant area of research in geometric function theory.
- Bernoulli polynomials have diverse applications in various mathematical fields.
Purpose of the Study:
- To introduce and investigate a new subclass of Te-univalent functions.
- To establish fundamental properties of this novel subclass, including coefficient bounds and inequalities.
Main Methods:
- Utilizing Bernoulli polynomials to define the new subclass.
- Applying established techniques in geometric function theory to derive coefficient bounds.
- Deriving the Fekete-Szegö inequality for the newly defined class.
Main Results:
- Introduction of a novel subclass of Te-univalent functions.
- Determination of initial coefficient bounds for the subclass.
- Establishment of the Fekete-Szegö inequality for the class.
Conclusions:
- The study successfully defines a new subclass of Te-univalent functions.
- The derived coefficient bounds and Fekete-Szegö inequality provide valuable insights into the properties of this subclass.
- Further corollaries enhance the understanding of the subclass's characteristics.
Related Concept Videos
00:59Bernoulli's Equation
10.1K
In the middle of the nineteenth century, it was observed that two trains passing each other at a high relative speed get pulled towards each other. The same occurs when two cars pass each other at a high relative speed. The reason is that the fluid pressure drops in the region where the fluid speeds up. As the air between the trains or the cars increases in speed, its pressure reduces. The pressure on the outer parts of the vehicles is still the atmospheric pressure, while the resultant...
10.1K
01:17Bernoulli's Principle: Applications
3.3K
There are many devices and situations in which fluid flows at a constant height and so can be analyzed using Bernoulli's principle. These devices include, but are not limited to, entrainment devices and fluid flow measuring devices.
Entrainment devices use a high fluid speed to create low pressures and, thus, entrain one fluid into another. Some examples of these devices are given below:
Entrainment devices use a high fluid speed to create low pressures and, thus, entrain one fluid into another. Some examples of these devices are given below:
3.3K
01:16Bernoulli's Equation: Problem Solving
793
A Venturi meter is essential for measuring fluid flow rates in pipelines. It utilizes the relationship between fluid velocity and pressure described by Bernoulli's equation. When installed in a sewage system, the Venturi meter accurately determines the wastewater flow rate by measuring pressure differences.
The first step is to compute the cross-sectional areas of the pipe and the Venturi throat to analyze the pressure difference indicated by the pressure gauge. Next, the continuity...
The first step is to compute the cross-sectional areas of the pipe and the Venturi throat to analyze the pressure difference indicated by the pressure gauge. Next, the continuity...
793
01:19Routh-Hurwitz Criterion II
182
In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
182
01:22Second Derivatives and Laplace Operator
1.2K
The first order operators using the del operator include the gradient, divergence and curl. Certain combinations of first order operators on a scalar or vector function yield second order expressions. Second-order expressions play a very important role in mathematics and physics. Some second order expressions include the divergence and curl of a gradient function, the divergence and curl of a curl function, and the gradient of a divergence function.
Consider a scalar function. The curl of its...
Consider a scalar function. The curl of its...
1.2K
01:10Theorems of Pappus and Guldinus
1.8K
The two theorems developed by Pappus and Guldinus are widely used in mathematics, engineering, and physics to find the surface area and volume of any body of revolution. This is done by revolving a plane curve around an axis that does not intersect the curve to find its surface area or revolving a plane area around a non-intersecting axis to calculate its volume.
For finding the surface area, consider a differential line element that generates a ring with surface area dA when revolved.
For finding the surface area, consider a differential line element that generates a ring with surface area dA when revolved.
1.8K